What is ln((3x+1+sqrt(9x^2+6x-8))/3) ?

The solution to ln((3x+1+sqrt(9x^2+6x-8))/3) is ln(3x+1+sqrt(9x^2+6x-8))-ln(3)

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simplify ln((3x+1+sqrt(9x^2+6x-8))/3)

simplify

ln (\frac{3 x + 1 + 9 x ^{2} + 6 x - 8}{3})

ln (3 x + 1 + 9 x^{2} + 6 x - 8) - ln (3)

Solution steps

ln (\frac{3 x + 1 + 9 x ^{2} + 6 x - 8}{3})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{3 x + 1 + 9 x ^{2} + 6 x - 8}{3}) = ln (3 x + 1 + 9 x^{2} + 6 x - 8) - ln (3)

= ln (3 x + 9 x^{2} + 6 x - 8 + 1) - ln (3)

ln (\frac{3.64}{23}) + (\frac{6}{23})

\frac{1}{2} ln (40) + \frac{1}{2} ln (1 - \frac{1}{2})

\frac{1}{3} (lo g_{a} (2 x^{2}) - lo g_{a} (b y^{5}))

ln (ib)

- lo g_{10} (4.56 \cdot 1 0^{- 6})

What is ln((3x+1+sqrt(9x^2+6x-8))/3) ?
The solution to ln((3x+1+sqrt(9x^2+6x-8))/3) is ln(3x+1+sqrt(9x^2+6x-8))-ln(3)